I think /u/coolduckingcool has the right idea based on your goals.

• Fly into Boston
• > Amtrak train to Mystic
• > MetroNorth train to New Haven and/or Stamford (I’m partial to Stamford but either or both would be worth checking out)
• > MetroNorth train to NYC
• Fly out of JFK

You’ll hit 4-5 solid towns/cities, each a bit different.

MetroNorth is significantly cheaper than Amtrak, doesn’t require you to pre-book tickets, and runs more frequently. So that would be your best bet for getting along the coast and into NYC, though technically you could take Amtrak if you really wanted to.

Personally I would skip New Haven and just go from Mystic to Stamford, mainly due to its proximity to NYC. One less separate lodging expense. And you can easily get to JFK from Stamford (if you didn’t want to spend the night in the city), though for that I would use an Uber instead of the trains as there’s no direct route to JFK and it just takes longer by public transport.